Progress on the modeling of liquid metal, free surface, MHD flows for fusion liquid walls

The proposed use of a flowing liquid metal layers as virtual first-walls for magnetic fusion energy reactors has prompted the development of numerical models capable of predicting the motion of such free surface liquid-metal flows within complex geometry boundaries and in the presence of strong magnetic fields. Several model variants were developed that utilize the assumption of toroidal axisymmetry to simplify the governing Navier-Stokes and Maxwell's equations to a 2D form. Typically an induced magnetic field formulation has been used to model eddy current formation and various numerical methods and free surface tracking techniques (including height function and volume-of-fluid) have been employed. These axisymmetric models predict a variety of interesting behavior including the effect of toroidal field gradients on the velocity profiles and stability, and the effect of surface-normal magnetic field components on toroidal motion and flow thickness. However, axisymmetric models cannot be used to simulate the true 3D geometry and magnetic field configuration of a magnetic fusion reactor. And so, a 3D, flexible geometry, multiple material, free surface magnetohydrodynamic (MHD) solver called HIMAG has been developed over the past several years. The HIMAG formulation is described in detail along with the results of several initial benchmark problems. Preliminary data from the application of HIMAG to several fusion relevant liquid wall problems including: (1) motion of lithium in a new sample holder for the Diverter Materials Evaluation System (DiMES) experiment on the DIII-D tokamak facility; (2) motion of gallium alloy in a quasi-2D film flow test section in the MTOR facility; (3) motion of gallium alloy in a 3D field film flow test section in the MTOR facility; are also presented and discussed. Finally, future plans for the HIMAG code, including application to the simulation of the effect of insulator coating cracks on closed channel MHD flows, are described.